Elliott, CM, Ranner, T orcid.org/0000-0001-7682-3175 and Venkataraman, C (2017) Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. SIAM Journal on Mathematical Analysis, 49 (1). pp. 360-397. ISSN 0036-1410
Abstract
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface resident receptors and ligands present in the extra-cellular medium. We prove the existence and uniqueness of solutions. We also consider a number of biologically relevant asymptotic limits of the model. We prove convergence to limiting problems which take the form of free boundary problems posed on the cell surface. We also report on numerical simulations illustrating convergence to one of the limiting problems as well as the spatio-temporal distributions of the receptors and ligands in a realistic geometry.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017, SIAM. Unauthorized reproduction of this article is prohibited. This is an author produced version of a paper published in SIAM Journal on Mathematical Analysis. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Receptor-ligand dynamics , bulk-surface PDEs , free boundary problems , bulk-surface finite elements |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Nov 2016 12:43 |
Last Modified: | 03 Dec 2018 13:43 |
Published Version: | http://doi.org/10.1137/15M1050811 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/15M1050811 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92970 |